{"id":"https://openalex.org/W7133194845","doi":"https://doi.org/10.1109/tit.2026.3669230","title":"Constructions of Combinatorial Neural Codes With Asymmetric Discrepancy","display_name":"Constructions of Combinatorial Neural Codes With Asymmetric Discrepancy","publication_year":2026,"publication_date":"2026-03-02","ids":{"openalex":"https://openalex.org/W7133194845","doi":"https://doi.org/10.1109/tit.2026.3669230"},"language":null,"primary_location":{"id":"doi:10.1109/tit.2026.3669230","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2026.3669230","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5127827944","display_name":"Zhonghua Sun","orcid":null},"institutions":[{"id":"https://openalex.org/I16365422","display_name":"Hefei University of Technology","ror":"https://ror.org/02czkny70","country_code":"CN","type":"education","lineage":["https://openalex.org/I16365422"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhonghua Sun","raw_affiliation_strings":["School of Mathematics, Hefei University of Technology, Hefei, Anhui, China"],"raw_orcid":"https://orcid.org/0000-0002-8975-1163","affiliations":[{"raw_affiliation_string":"School of Mathematics, Hefei University of Technology, Hefei, Anhui, China","institution_ids":["https://openalex.org/I16365422"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5127830734","display_name":"Xinxin Song","orcid":null},"institutions":[{"id":"https://openalex.org/I16365422","display_name":"Hefei University of Technology","ror":"https://ror.org/02czkny70","country_code":"CN","type":"education","lineage":["https://openalex.org/I16365422"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinxin Song","raw_affiliation_strings":["School of Mathematics, Hefei University of Technology, Hefei, Anhui, China"],"raw_orcid":"https://orcid.org/0009-0009-5776-198X","affiliations":[{"raw_affiliation_string":"School of Mathematics, Hefei University of Technology, Hefei, Anhui, China","institution_ids":["https://openalex.org/I16365422"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5123742127","display_name":"Yang Li","orcid":null},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Yang Li","raw_affiliation_strings":["School of Physical and Mathematical Sciences, Nanyang Technological University, Nanyang Ave, Singapore"],"raw_orcid":"https://orcid.org/0000-0003-0286-9263","affiliations":[{"raw_affiliation_string":"School of Physical and Mathematical Sciences, Nanyang Technological University, Nanyang Ave, Singapore","institution_ids":["https://openalex.org/I172675005"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.35984481,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"72","issue":"5","first_page":"2949","last_page":"2962"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.3711000084877014,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.3711000084877014,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.17309999465942383,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.10109999775886536,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.7190999984741211},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.6543999910354614},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.6064000129699707},{"id":"https://openalex.org/keywords/binary-code","display_name":"Binary code","score":0.5961999893188477},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.48010000586509705},{"id":"https://openalex.org/keywords/equidistant","display_name":"Equidistant","score":0.4765999913215637},{"id":"https://openalex.org/keywords/expander-code","display_name":"Expander code","score":0.476500004529953},{"id":"https://openalex.org/keywords/reed\u2013muller-code","display_name":"Reed\u2013Muller code","score":0.46650001406669617}],"concepts":[{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.7190999984741211},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.6543999910354614},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.6064000129699707},{"id":"https://openalex.org/C63435697","wikidata":"https://www.wikidata.org/wiki/Q864135","display_name":"Binary code","level":3,"score":0.5961999893188477},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5871999859809875},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5449000000953674},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5131999850273132},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.48010000586509705},{"id":"https://openalex.org/C158245278","wikidata":"https://www.wikidata.org/wiki/Q4386982","display_name":"Equidistant","level":2,"score":0.4765999913215637},{"id":"https://openalex.org/C108509264","wikidata":"https://www.wikidata.org/wiki/Q5420758","display_name":"Expander code","level":5,"score":0.476500004529953},{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.46650001406669617},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.4174000024795532},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.3928999900817871},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.3691999912261963},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.3594000041484833},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3278000056743622},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30799999833106995},{"id":"https://openalex.org/C3427991","wikidata":"https://www.wikidata.org/wiki/Q651426","display_name":"Group code","level":5,"score":0.30390000343322754},{"id":"https://openalex.org/C85307737","wikidata":"https://www.wikidata.org/wiki/Q751969","display_name":"Coset","level":2,"score":0.30230000615119934},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.2888000011444092},{"id":"https://openalex.org/C122451846","wikidata":"https://www.wikidata.org/wiki/Q5150824","display_name":"Combinatorial design","level":2,"score":0.2822999954223633},{"id":"https://openalex.org/C63361517","wikidata":"https://www.wikidata.org/wiki/Q5645805","display_name":"Hamming weight","level":5,"score":0.25049999356269836}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2026.3669230","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2026.3669230","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.6974653005599976}],"awards":[{"id":"https://openalex.org/G1853049553","display_name":null,"funder_award_id":"U21A20428","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2343940317","display_name":null,"funder_award_id":"12571573","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2817085005","display_name":null,"funder_award_id":"JZ2024HGTB0203","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G7290790642","display_name":null,"funder_award_id":"2408085MA014","funder_id":"https://openalex.org/F4320334897","funder_display_name":"Natural Science Foundation of Anhui Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334897","display_name":"Natural Science Foundation of Anhui Province","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,45],"recent":[1],"work":[2],"by":[3,42,167],"Cotardo":[4],"and":[5,39,52,61,78,91,131,146],"Ravagnani":[6],"(IEEE":[7],"Trans.":[8],"Inf.":[9],"Theory,":[10],"vol.":[11],"68,":[12],"no.":[13],"5,":[14],"pp.":[15],"2941-2950,":[16],"May":[17],"2022)":[18],"introduced":[19],"a":[20,96],"class":[21],"of":[22,82,114,164],"binary":[23,48,59,97],"codes":[24,36,60,77,85,90,166,170],"endowed":[25],"with":[26],"asymmetric":[27,49,67,112],"discrepancy,":[28],"which":[29],"are":[30,40],"referred":[31],"to":[32],"as":[33],"Combinatorial":[34],"Neural":[35],"(CN":[37],"codes),":[38],"motivated":[41],"theoretical":[43],"neuroscience.":[44],"applications":[46],"in":[47,57],"memoryless":[50],"channel":[51],"neuroscience":[53],"have":[54],"spurred":[55],"interest":[56],"constructing":[58],"analyzing":[62],"the":[63,88,110,115,121,132,143,148,158],"error-correction":[64],"capabilities":[65],"under":[66],"discrepancy.":[68],"In":[69],"this":[70],"paper,":[71],"we":[72,107,155],"first":[73],"characterize":[74],"equidistant":[75],"CN":[76,84,165],"propose":[79],"several":[80,162],"constructions":[81],"(equidistant)":[83],"based":[86],"on":[87,152],"Hadamard":[89,93],"punctured":[92],"codes.":[94,174],"For":[95],"linear":[98],"code":[99],"<italic":[100,118,134],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[101,105,119,124,129,135,138],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">C</i>":[102,125,136],"\u2286":[103],"GF(2)<italic":[104,128],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><sup>n</sup></i>,":[106],"then":[108],"analyze":[109],"minimum":[111],"discrepancy":[113],"nonzero":[116],"subset":[117],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">C</i>\\{0},":[120],"coset":[122],"u+<italic":[123],"(u":[126],"\u2208":[127],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><sup>n</sup></i>),":[130],"union":[133],"\u222a(1+<italic":[137],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">C</i>),":[139],"where":[140],"0":[141],"denotes":[142],"all-zero":[144],"vector":[145],"1":[147],"all-one":[149],"vector.":[150],"Based":[151],"these":[153],"results,":[154],"completely":[156],"determine":[157],"exact":[159],"parameters":[160],"for":[161],"classes":[163],"combining":[168],"simplex":[169],"or":[171],"projective":[172],"2-weight":[173]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-03-03T00:00:00"}
